ICERM Semester Program on "Model and dimension reduction in uncertain and dynamic systems"
(January 27 - May 1, 2020)
Today’s computational and experimental paradigms feature complex models along with disparate and, frequently, enormous data sets. This necessitates the development of theoretical and computational strategies for efficient and robust numerical algorithms that effectively resolve the important features and characteristics of these complex computational models. The desiderata for resolving the underlying model features is often application-specific and combines mathematical tasks like approximation, prediction, calibration, design, and optimization. Running simulations that fully account for the variability of the complexities of modern scientific models can be infeasible due to the curse of dimensionality, chaotic behavior or dynamics, and/or overwhelming streams of informative data.
This semester program focuses on both theoretical investigation and practical algorithm development for reduction in the complexity – the dimension, the degrees of freedom, the data – arising in these models. The four broad thrusts of the program are (1) Mathematics of reduced order models, (2) Algorithms for approximation and complexity reduction, (3) Computational statistics and data-driven techniques, and (4) Application-specific design. The particular topics include classical strategies such as parametric sensitivity analysis and best approximations, mature but active topics like principal component analysis and information-based complexity, and promising nascent topics such as layered neural networks and high-dimensional statistics.
This program will integrate diverse fields of mathematical analysis, statistical sciences, data and computer science, and specifically attract researchers working on model order reduction, data-driven model calibration and simplification, computations and approximations in high dimensions, and data-intensive uncertainty quantification. Various workshops will be designed to stimulate interaction between these research areas and establish cross-disciplinary collaboration. Investigation and assimilation of complementary approaches through other program events will achieve cross-fertilization and serve as a nexus for multiple research communities.